We investigate projective estimation under model inadequacies, i.e., when the underpinning assumptions of the projective model are not fully satisfied by the data. We focus on the task of image stitching which is customarily solved by estimating a projective warp - a model that is justified when the scene is planar or when the views differ purely by rotation. Such conditions are easily violated in practice, and this yields stitching results with ghosting artefacts that necessitate the usage of deghosting algorithms. To this end we propose as-projective-as-possible warps, i.e., warps that aim to be globally projective, yet allow local non-projective deviations to account for violations to the assumed imaging conditions. Based on a novel estimation technique called Moving Direct Linear Transformation (Moving DLT), our method seamlessly bridges image regions that are inconsistent with the projective model. The result is highly accurate image stitching, with significantly reduced ghosting effects, thus lowering the dependency on post hoc deghosting.